%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : AGT025+2 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:06:38 AM UTC 2026
% Result : Theorem 6.20s 1.67s
% Output : Refutation 7.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 24
% Syntax : Number of formulae : 95 ( 45 unt; 2 def)
% Number of atoms : 207 ( 0 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 203 ( 91 ~; 85 |; 19 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 3 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 19 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn 85 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2,X3] :
( ( accept_population(X0,X3,X1)
& less(X2,X1) )
=> accept_population(X0,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1_3) ).
fof(f16,axiom,
! [X0] :
( ( accept_population(X0,atheist,n75)
& accept_population(X0,christian,n24)
& accept_population(X0,muslim,n1)
& accept_population(X0,native,n0)
& accept_population(X0,other,n0) )
<=> accept_city(X0,towna) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_9) ).
fof(f362,axiom,
accept_population(muslimcountrybhumanitarianorganization,other,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',deduced_93) ).
fof(f472,axiom,
accept_population(muslimcountrybhumanitarianorganization,native,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',deduced_203) ).
fof(f473,axiom,
accept_population(muslimcountrybhumanitarianorganization,muslim,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',deduced_204) ).
fof(f475,axiom,
accept_population(muslimcountrybhumanitarianorganization,atheist,n78),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',deduced_206) ).
fof(f635,axiom,
~ accept_city(muslimcountrybhumanitarianorganization,towna),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',deduced_366) ).
fof(f661,axiom,
rdn_translate(n24,rdn_pos(rdn(rdnn(n4),rdnn(n2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn24) ).
fof(f662,axiom,
rdn_translate(n25,rdn_pos(rdn(rdnn(n5),rdnn(n2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn25) ).
fof(f712,axiom,
rdn_translate(n75,rdn_pos(rdn(rdnn(n5),rdnn(n7)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn75) ).
fof(f715,axiom,
rdn_translate(n78,rdn_pos(rdn(rdnn(n8),rdnn(n7)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn78) ).
fof(f894,axiom,
rdn_non_zero_digit(rdnn(n2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit2) ).
fof(f899,axiom,
rdn_non_zero_digit(rdnn(n7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit7) ).
fof(f906,axiom,
rdn_positive_less(rdnn(n4),rdnn(n5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less45) ).
fof(f907,axiom,
rdn_positive_less(rdnn(n5),rdnn(n6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less56) ).
fof(f908,axiom,
rdn_positive_less(rdnn(n6),rdnn(n7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less67) ).
fof(f909,axiom,
rdn_positive_less(rdnn(n7),rdnn(n8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less78) ).
fof(f911,axiom,
! [X0,X1,X2] :
( ( rdn_positive_less(rdnn(X0),rdnn(X1))
& rdn_positive_less(rdnn(X1),rdnn(X2)) )
=> rdn_positive_less(rdnn(X0),rdnn(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less_transitivity) ).
fof(f913,axiom,
! [X0,X1,X2] :
( ( rdn_positive_less(rdnn(X0),rdnn(X2))
& rdn_non_zero(X1) )
=> rdn_positive_less(rdn(rdnn(X0),X1),rdn(rdnn(X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less_multi_digit_low) ).
fof(f915,axiom,
! [X0] :
( rdn_non_zero_digit(rdnn(X0))
=> rdn_non_zero(rdnn(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_non_zero_by_digit) ).
fof(f917,axiom,
! [X0,X1,X2,X3] :
( ( rdn_translate(X0,rdn_pos(X2))
& rdn_translate(X1,rdn_pos(X3))
& rdn_positive_less(X2,X3) )
=> less(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_entry_point_pos_pos) ).
fof(f923,conjecture,
? [X0,X1] : ~ accept_population(X0,X1,n25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',query_25) ).
fof(f924,negated_conjecture,
~ ? [X0,X1] : ~ accept_population(X0,X1,n25),
inference(negated_conjecture,[status(cth)],[f923]) ).
fof(f931,plain,
! [X0,X1,X2,X3] :
( accept_population(X0,X3,X2)
| ~ accept_population(X0,X3,X1)
| ~ less(X2,X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f932,plain,
! [X0,X1,X2,X3] :
( accept_population(X0,X3,X2)
| ~ accept_population(X0,X3,X1)
| ~ less(X2,X1) ),
inference(flattening,[],[f931]) ).
fof(f937,plain,
! [X0,X1,X2] :
( rdn_positive_less(rdnn(X0),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1))
| ~ rdn_positive_less(rdnn(X1),rdnn(X2)) ),
inference(ennf_transformation,[],[f911]) ).
fof(f938,plain,
! [X0,X1,X2] :
( rdn_positive_less(rdnn(X0),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1))
| ~ rdn_positive_less(rdnn(X1),rdnn(X2)) ),
inference(flattening,[],[f937]) ).
fof(f940,plain,
! [X0,X1,X2] :
( rdn_positive_less(rdn(rdnn(X0),X1),rdn(rdnn(X2),X1))
| ~ rdn_positive_less(rdnn(X0),rdnn(X2))
| ~ rdn_non_zero(X1) ),
inference(ennf_transformation,[],[f913]) ).
fof(f941,plain,
! [X0,X1,X2] :
( rdn_positive_less(rdn(rdnn(X0),X1),rdn(rdnn(X2),X1))
| ~ rdn_positive_less(rdnn(X0),rdnn(X2))
| ~ rdn_non_zero(X1) ),
inference(flattening,[],[f940]) ).
fof(f943,plain,
! [X0] :
( rdn_non_zero(rdnn(X0))
| ~ rdn_non_zero_digit(rdnn(X0)) ),
inference(ennf_transformation,[],[f915]) ).
fof(f945,plain,
! [X0,X1,X2,X3] :
( less(X0,X1)
| ~ rdn_translate(X0,rdn_pos(X2))
| ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_positive_less(X2,X3) ),
inference(ennf_transformation,[],[f917]) ).
fof(f946,plain,
! [X0,X1,X2,X3] :
( less(X0,X1)
| ~ rdn_translate(X0,rdn_pos(X2))
| ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_positive_less(X2,X3) ),
inference(flattening,[],[f945]) ).
fof(f951,plain,
! [X0,X1] : accept_population(X0,X1,n25),
inference(ennf_transformation,[],[f924]) ).
fof(f970,plain,
! [X0] :
( ( ( accept_population(X0,atheist,n75)
& accept_population(X0,christian,n24)
& accept_population(X0,muslim,n1)
& accept_population(X0,native,n0)
& accept_population(X0,other,n0) )
| ~ accept_city(X0,towna) )
& ( accept_city(X0,towna)
| ~ accept_population(X0,atheist,n75)
| ~ accept_population(X0,christian,n24)
| ~ accept_population(X0,muslim,n1)
| ~ accept_population(X0,native,n0)
| ~ accept_population(X0,other,n0) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f971,plain,
! [X0] :
( ( ( accept_population(X0,atheist,n75)
& accept_population(X0,christian,n24)
& accept_population(X0,muslim,n1)
& accept_population(X0,native,n0)
& accept_population(X0,other,n0) )
| ~ accept_city(X0,towna) )
& ( accept_city(X0,towna)
| ~ accept_population(X0,atheist,n75)
| ~ accept_population(X0,christian,n24)
| ~ accept_population(X0,muslim,n1)
| ~ accept_population(X0,native,n0)
| ~ accept_population(X0,other,n0) ) ),
inference(flattening,[],[f970]) ).
fof(f987,plain,
! [X2,X3,X0,X1] :
( ~ accept_population(X0,X3,X1)
| accept_population(X0,X3,X2)
| ~ less(X2,X1) ),
inference(cnf_transformation,[],[f932]) ).
fof(f1040,plain,
! [X0] :
( ~ accept_population(X0,other,n0)
| ~ accept_population(X0,atheist,n75)
| ~ accept_population(X0,christian,n24)
| ~ accept_population(X0,muslim,n1)
| ~ accept_population(X0,native,n0)
| accept_city(X0,towna) ),
inference(cnf_transformation,[],[f971]) ).
fof(f1411,plain,
accept_population(muslimcountrybhumanitarianorganization,other,n0),
inference(cnf_transformation,[],[f362]) ).
fof(f1521,plain,
accept_population(muslimcountrybhumanitarianorganization,native,n0),
inference(cnf_transformation,[],[f472]) ).
fof(f1522,plain,
accept_population(muslimcountrybhumanitarianorganization,muslim,n1),
inference(cnf_transformation,[],[f473]) ).
fof(f1524,plain,
accept_population(muslimcountrybhumanitarianorganization,atheist,n78),
inference(cnf_transformation,[],[f475]) ).
fof(f1684,plain,
~ accept_city(muslimcountrybhumanitarianorganization,towna),
inference(cnf_transformation,[],[f635]) ).
fof(f1710,plain,
rdn_translate(n24,rdn_pos(rdn(rdnn(n4),rdnn(n2)))),
inference(cnf_transformation,[],[f661]) ).
fof(f1711,plain,
rdn_translate(n25,rdn_pos(rdn(rdnn(n5),rdnn(n2)))),
inference(cnf_transformation,[],[f662]) ).
fof(f1761,plain,
rdn_translate(n75,rdn_pos(rdn(rdnn(n5),rdnn(n7)))),
inference(cnf_transformation,[],[f712]) ).
fof(f1764,plain,
rdn_translate(n78,rdn_pos(rdn(rdnn(n8),rdnn(n7)))),
inference(cnf_transformation,[],[f715]) ).
fof(f1943,plain,
rdn_non_zero_digit(rdnn(n2)),
inference(cnf_transformation,[],[f894]) ).
fof(f1948,plain,
rdn_non_zero_digit(rdnn(n7)),
inference(cnf_transformation,[],[f899]) ).
fof(f1955,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(cnf_transformation,[],[f906]) ).
fof(f1956,plain,
rdn_positive_less(rdnn(n5),rdnn(n6)),
inference(cnf_transformation,[],[f907]) ).
fof(f1957,plain,
rdn_positive_less(rdnn(n6),rdnn(n7)),
inference(cnf_transformation,[],[f908]) ).
fof(f1958,plain,
rdn_positive_less(rdnn(n7),rdnn(n8)),
inference(cnf_transformation,[],[f909]) ).
fof(f1960,plain,
! [X2,X0,X1] :
( ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1))
| rdn_positive_less(rdnn(X0),rdnn(X2)) ),
inference(cnf_transformation,[],[f938]) ).
fof(f1962,plain,
! [X2,X0,X1] :
( rdn_positive_less(rdn(rdnn(X0),X1),rdn(rdnn(X2),X1))
| ~ rdn_positive_less(rdnn(X0),rdnn(X2))
| ~ rdn_non_zero(X1) ),
inference(cnf_transformation,[],[f941]) ).
fof(f1964,plain,
! [X0] :
( ~ rdn_non_zero_digit(rdnn(X0))
| rdn_non_zero(rdnn(X0)) ),
inference(cnf_transformation,[],[f943]) ).
fof(f1966,plain,
! [X2,X3,X0,X1] :
( ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_pos(X2))
| less(X0,X1)
| ~ rdn_positive_less(X2,X3) ),
inference(cnf_transformation,[],[f946]) ).
fof(f1972,plain,
! [X0,X1] : accept_population(X0,X1,n25),
inference(cnf_transformation,[],[f951]) ).
fof(f1977,plain,
! [X0,X1] :
( ~ rdn_positive_less(X1,rdn(rdnn(n5),rdnn(n2)))
| less(X0,n25)
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(resolution,[],[f1966,f1711]) ).
fof(f1980,plain,
( ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n1)
| ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
| accept_city(muslimcountrybhumanitarianorganization,towna) ),
inference(resolution,[],[f1411,f1040]) ).
fof(f1981,plain,
( ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
| accept_city(muslimcountrybhumanitarianorganization,towna) ),
inference(forward_subsumption_resolution,[],[f1980,f1522]) ).
fof(f1982,plain,
( ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| accept_city(muslimcountrybhumanitarianorganization,towna) ),
inference(forward_subsumption_resolution,[],[f1981,f1521]) ).
fof(f1983,plain,
( ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n24) ),
inference(forward_subsumption_resolution,[],[f1982,f1684]) ).
fof(f1985,definition,
( spl0_1
<=> accept_population(muslimcountrybhumanitarianorganization,christian,n24) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f1987,plain,
( ~ accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| spl0_1 ),
inference(avatar_component_clause,[],[f1985]) ).
fof(f1989,definition,
( spl0_2
<=> accept_population(muslimcountrybhumanitarianorganization,atheist,n75) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f1991,plain,
( ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| spl0_2 ),
inference(avatar_component_clause,[],[f1989]) ).
fof(f1992,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f1983,f1989,f1985]) ).
fof(f2016,plain,
rdn_non_zero(rdnn(n2)),
inference(resolution,[],[f1964,f1943]) ).
fof(f2022,plain,
rdn_non_zero(rdnn(n7)),
inference(resolution,[],[f1948,f1964]) ).
fof(f2026,plain,
! [X0,X1] :
( ~ rdn_positive_less(rdnn(X0),rdnn(n5))
| ~ rdn_non_zero(rdnn(n2))
| less(X1,n25)
| ~ rdn_translate(X1,rdn_pos(rdn(rdnn(X0),rdnn(n2)))) ),
inference(resolution,[],[f1962,f1977]) ).
fof(f2027,plain,
! [X0,X1] :
( ~ rdn_translate(X1,rdn_pos(rdn(rdnn(X0),rdnn(n2))))
| less(X1,n25)
| ~ rdn_positive_less(rdnn(X0),rdnn(n5)) ),
inference(forward_subsumption_resolution,[],[f2026,f2016]) ).
fof(f2028,plain,
( less(n24,n25)
| ~ rdn_positive_less(rdnn(n4),rdnn(n5)) ),
inference(resolution,[],[f2027,f1710]) ).
fof(f2031,plain,
less(n24,n25),
inference(forward_subsumption_resolution,[],[f2028,f1955]) ).
fof(f2074,plain,
! [X2,X0,X1] :
( accept_population(X0,X1,X2)
| ~ less(X2,n25) ),
inference(resolution,[],[f987,f1972]) ).
fof(f2100,plain,
! [X0] :
( accept_population(muslimcountrybhumanitarianorganization,atheist,X0)
| ~ less(X0,n78) ),
inference(resolution,[],[f987,f1524]) ).
fof(f2117,plain,
( ~ less(n24,n25)
| spl0_1 ),
inference(resolution,[],[f2074,f1987]) ).
fof(f2119,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f2117,f2031]) ).
fof(f2120,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f2119]) ).
fof(f2138,plain,
( ~ less(n75,n78)
| spl0_2 ),
inference(resolution,[],[f2100,f1991]) ).
fof(f2145,plain,
! [X0] :
( ~ rdn_positive_less(rdnn(X0),rdnn(n7))
| rdn_positive_less(rdnn(X0),rdnn(n8)) ),
inference(resolution,[],[f1960,f1958]) ).
fof(f2153,plain,
! [X0] :
( ~ rdn_positive_less(rdnn(X0),rdnn(n6))
| rdn_positive_less(rdnn(X0),rdnn(n7)) ),
inference(resolution,[],[f1960,f1957]) ).
fof(f2159,plain,
rdn_positive_less(rdnn(n5),rdnn(n7)),
inference(resolution,[],[f2153,f1956]) ).
fof(f2160,plain,
rdn_positive_less(rdnn(n5),rdnn(n8)),
inference(resolution,[],[f2159,f2145]) ).
fof(f2315,plain,
! [X0,X1] :
( ~ rdn_positive_less(X1,rdn(rdnn(n8),rdnn(n7)))
| less(X0,n78)
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(resolution,[],[f1764,f1966]) ).
fof(f2326,plain,
! [X0,X1] :
( less(X0,n78)
| ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(n7))))
| ~ rdn_positive_less(rdnn(X1),rdnn(n8))
| ~ rdn_non_zero(rdnn(n7)) ),
inference(resolution,[],[f2315,f1962]) ).
fof(f2328,plain,
! [X0,X1] :
( ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(n7))))
| less(X0,n78)
| ~ rdn_positive_less(rdnn(X1),rdnn(n8)) ),
inference(forward_subsumption_resolution,[],[f2326,f2022]) ).
fof(f2334,plain,
( less(n75,n78)
| ~ rdn_positive_less(rdnn(n5),rdnn(n8)) ),
inference(resolution,[],[f2328,f1761]) ).
fof(f2337,plain,
( ~ rdn_positive_less(rdnn(n5),rdnn(n8))
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f2334,f2138]) ).
fof(f2338,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f2337,f2160]) ).
fof(f2339,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f2338]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f1992]) ).
cnf(s4,plain,
spl0_1,
inference(sat_conversion,[],[f2120]) ).
cnf(s11,plain,
spl0_2,
inference(sat_conversion,[],[f2339]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s11,s4]) ).
fof(f2340,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : AGT025+2 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n001.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 19:20:04 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.44/1.58 % (638801)Detected formulas, will run a generic FOF schedule.
% 5.44/1.58 % (638806)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1702603922:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.44/1.58 % (638808)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2546365976:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.44/1.58 % (638812)dis-21_1_sil=8000:lcm=predicate:random_seed=2871282782:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 5.44/1.58 % (638809)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2533046286:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.44/1.58 % (638807)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=567303402:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.44/1.58 % (638810)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=681987333:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.44/1.58 % (638810)Refutation not found, incomplete strategy
% 5.44/1.58 % (638810)------------------------------
% 5.44/1.58 % (638810)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.44/1.58 % (638810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.44/1.58 % (638809)Refutation not found, incomplete strategy
% 5.44/1.58 % (638809)------------------------------
% 5.44/1.58 % (638809)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.44/1.58 % (638810)CaDiCaL version: 2.1.3
% 5.44/1.58 % (638810)Termination reason: Refutation not found, incomplete strategy
% 5.44/1.58 % (638810)Time elapsed: 0.002 s
% 5.44/1.58 % (638810)Peak memory usage: 87 MB
% 5.44/1.58 % (638809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.44/1.58 % (638810)Instructions burned: 2 (million)
% 5.44/1.58 % (638809)CaDiCaL version: 2.1.3
% 5.44/1.58 % (638809)Termination reason: Refutation not found, incomplete strategy
% 5.44/1.58 % (638809)Time elapsed: 0.002 s
% 5.44/1.58 % (638809)Peak memory usage: 87 MB
% 5.44/1.58 % (638809)Instructions burned: 2 (million)
% 5.44/1.58 % (638811)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3222959274:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.44/1.58 % (638812)Instruction limit reached!
% 5.44/1.58 % (638812)------------------------------
% 5.44/1.58 % (638812)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.44/1.58 % (638812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.44/1.58 % (638812)CaDiCaL version: 2.1.3
% 5.44/1.58 % (638812)Termination reason: Instruction limit
% 5.44/1.58 % (638812)Termination phase: Saturation
% 5.44/1.58 % (638812)Time elapsed: 0.063 s
% 5.44/1.58 % (638812)Peak memory usage: 90 MB
% 5.44/1.58 % (638812)Instructions burned: 129 (million)
% 5.44/1.58 % (638811)Instruction limit reached!
% 5.44/1.58 % (638811)------------------------------
% 5.44/1.58 % (638811)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.44/1.58 % (638811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.44/1.58 % (638811)CaDiCaL version: 2.1.3
% 5.44/1.58 % (638811)Termination reason: Instruction limit
% 5.44/1.58 % (638811)Termination phase: Saturation
% 5.44/1.58 % (638811)Time elapsed: 0.080 s
% 5.44/1.58 % (638811)Peak memory usage: 90 MB
% 5.44/1.58 % (638811)Instructions burned: 140 (million)
% 5.44/1.58 % (638820)lrs+10_1_sil=8000:sp=occurrence:random_seed=1876576949:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.44/1.58 % (638820)Refutation not found, incomplete strategy
% 5.44/1.58 % (638820)------------------------------
% 5.44/1.58 % (638820)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.44/1.58 % (638820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.44/1.58 % (638820)CaDiCaL version: 2.1.3
% 5.44/1.58 % (638820)Termination reason: Refutation not found, incomplete strategy
% 5.44/1.58 % (638820)Time elapsed: 0.008 s
% 5.44/1.58 % (638820)Peak memory usage: 89 MB
% 5.44/1.58 % (638820)Instructions burned: 13 (million)
% 5.44/1.58 % (638809)------------------------------
% 5.44/1.58 % (638809)------------------------------
% 6.20/1.67 % (638810)------------------------------
% 6.20/1.67 % (638810)------------------------------
% 6.20/1.67 % (638821)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2318452497:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.20/1.67 % (638821)Refutation not found, incomplete strategy
% 6.20/1.67 % (638821)------------------------------
% 6.20/1.67 % (638821)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.20/1.67 % (638821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.67 % (638821)CaDiCaL version: 2.1.3
% 6.20/1.67 % (638821)Termination reason: Refutation not found, incomplete strategy
% 6.20/1.67 % (638821)Time elapsed: 0.005 s
% 6.20/1.67 % (638821)Peak memory usage: 88 MB
% 6.20/1.67 % (638821)Instructions burned: 8 (million)
% 6.20/1.67 [W928 19:20:05.162789411 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 6.20/1.67 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.20/1.67 [W928 19:20:05.162827858 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 6.20/1.67 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.20/1.67 [W928 19:20:05.162866155 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 6.20/1.67 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.20/1.67 [W928 19:20:05.162879305 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 6.20/1.67 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.20/1.67 [W928 19:20:05.162906939 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 6.20/1.67 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.20/1.67 [W928 19:20:05.162918869 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 6.20/1.67 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.20/1.67 [W928 19:20:05.162944772 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 6.20/1.67 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.20/1.67 [W928 19:20:05.162956842 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 6.20/1.67 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.20/1.67 [W928 19:20:05.162982559 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 6.20/1.67 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.20/1.67 [W928 19:20:05.162994406 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 6.20/1.67 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.20/1.67 [W928 19:20:05.163031303 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 6.20/1.67 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.20/1.67 [W928 19:20:05.163043856 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 6.20/1.67 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.20/1.67 % (638824)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=208136142:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 6.20/1.67 % (638823)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1178056563:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 6.20/1.67 % (638823)Refutation not found, incomplete strategy
% 6.20/1.67 % (638823)------------------------------
% 6.20/1.67 % (638823)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.20/1.67 % (638823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.67 % (638823)CaDiCaL version: 2.1.3
% 6.20/1.67 % (638823)Termination reason: Refutation not found, incomplete strategy
% 6.20/1.67 % (638823)Time elapsed: 0.003 s
% 6.20/1.67 % (638823)Peak memory usage: 88 MB
% 6.20/1.67 % (638823)Instructions burned: 2 (million)
% 6.20/1.67 % (638824)Instruction limit reached!
% 6.20/1.67 % (638824)------------------------------
% 6.20/1.67 % (638824)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.20/1.67 % (638824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.67 % (638824)CaDiCaL version: 2.1.3
% 6.20/1.67 % (638824)Termination reason: Instruction limit
% 6.20/1.67 % (638824)Termination phase: Saturation
% 6.20/1.67 % (638824)Time elapsed: 0.069 s
% 6.20/1.67 % (638824)Peak memory usage: 91 MB
% 6.20/1.67 % (638824)Instructions burned: 250 (million)
% 6.20/1.67 % (638820)------------------------------
% 6.20/1.67 % (638820)------------------------------
% 6.20/1.67 % (638821)------------------------------
% 6.20/1.67 % (638821)------------------------------
% 6.20/1.67 % (638806)First to succeed.
% 6.20/1.67 % (638806)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-638801"
% 6.20/1.67 % (638808)Refutation not found, incomplete strategy
% 6.20/1.67 % (638808)------------------------------
% 6.20/1.67 % (638808)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.20/1.67 % (638808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.67 % (638808)CaDiCaL version: 2.1.3
% 6.20/1.67 % (638808)Termination reason: Refutation not found, incomplete strategy
% 6.20/1.67 % (638808)Time elapsed: 0.567 s
% 6.20/1.67 % (638808)Peak memory usage: 127 MB
% 6.20/1.67 % (638808)Instructions burned: 832 (million)
% 6.20/1.67 % (638828)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1074547639:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 6.20/1.67 % (638828)Refutation not found, incomplete strategy
% 6.20/1.67 % (638828)------------------------------
% 6.20/1.67 % (638828)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.20/1.67 % (638828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.67 % (638828)CaDiCaL version: 2.1.3
% 6.20/1.67 % (638828)Termination reason: Refutation not found, incomplete strategy
% 6.20/1.67 % (638828)Time elapsed: 0.004 s
% 6.20/1.67 % (638828)Peak memory usage: 88 MB
% 6.20/1.67 % (638828)Instructions burned: 12 (million)
% 6.20/1.67 % (638829)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2342311921:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 6.20/1.67 % (638823)------------------------------
% 6.20/1.67 % (638823)------------------------------
% 6.20/1.67 % (638830)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2433931501:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 6.20/1.67 % (638830)Refutation not found, incomplete strategy
% 6.20/1.67 % (638830)------------------------------
% 6.20/1.67 % (638830)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.20/1.67 % (638830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.67 % (638830)CaDiCaL version: 2.1.3
% 6.20/1.67 % (638830)Termination reason: Refutation not found, incomplete strategy
% 6.20/1.67 % (638830)Time elapsed: 0.006 s
% 6.20/1.67 % (638830)Peak memory usage: 88 MB
% 6.20/1.67 % (638830)Instructions burned: 9 (million)
% 6.20/1.67 % (638807)Refutation not found, incomplete strategy
% 6.20/1.67 % (638807)------------------------------
% 6.20/1.67 % (638807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.20/1.67 % (638807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.67 % (638807)CaDiCaL version: 2.1.3
% 6.20/1.67 % (638807)Termination reason: Refutation not found, incomplete strategy
% 6.20/1.67 % (638807)Time elapsed: 0.731 s
% 6.20/1.67 % (638807)Peak memory usage: 132 MB
% 6.20/1.67 % (638807)Instructions burned: 1082 (million)
% 6.20/1.67 % (638828)------------------------------
% 6.20/1.67 % (638828)------------------------------
% 6.20/1.67 % (638806)Refutation found. Thanks to Tanya!
% 6.20/1.67 % SZS status Theorem for theBenchmark
% 6.20/1.67 % SZS output start Proof for theBenchmark
% See solution above
% 7.59/1.86 % (638806)------------------------------
% 7.59/1.86 % (638806)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.59/1.86 % (638806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.59/1.86 % (638806)CaDiCaL version: 2.1.3
% 7.59/1.86 % (638806)Termination reason: Refutation
% 7.59/1.86 % (638806)Time elapsed: 0.578 s
% 7.59/1.86 % (638806)Peak memory usage: 138 MB
% 7.59/1.86 % (638806)Instructions burned: 1250 (million)
% 7.59/1.86 % (638806)------------------------------
% 7.59/1.86 % (638806)------------------------------
% 7.59/1.86 % (638801)Success in time 1.005 s
% 7.59/1.86 % Vampire exiting
%------------------------------------------------------------------------------